<TeXmacs|1.99.4>

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  <doc-data|<doc-title|2017-02-09-01>>

  <section|\<#9898\>\<#76EE\>>

  \<#53D1\>\<#9898\>\<#4EBA\>\<#FF1A\> \<#5FAE\>\<#4FE1\>\<#516C\>\<#4F17\>\<#53F7\>
  \P\<#6570\>\<#5B66\>\<#89E3\>\<#9898\>\<#4E4B\>\<#8DEF\>\Q

  \<#53D1\>\<#9898\>\<#65E5\>\<#671F\>: 2017-02-08

  \<#5982\>\<#56FE\>\<#FF0C\>\<#5206\>\<#522B\>\<#4EE5\>\<#4E09\>\<#89D2\>\<#5F62\><math|A
  B C>\<#7684\>\<#8FB9\><math|A B>\<#548C\><math|A
  C>\<#5411\>\<#5F62\>\<#5916\>\<#4F5C\>\<#6B63\>\<#65B9\>\<#5F62\>\<#FF0C\>\<#5176\>\<#4F59\>\<#5404\>\<#70B9\>\<#7684\>\<#610F\>\<#4E49\>\<#5982\>\<#56FE\>\<#6240\>\<#793A\>\<#FF0C\>\<#6C42\>\<#8BC1\>\<#FF1A\><math|S
  T>\<#4E0E\><math|P Q>\<#5E73\>\<#884C\>.

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  \;

  <section|\<#89E3\>\<#7B54\>>

  \<#89E3\>\<#7B54\>\<#8005\>\<#FF1A\> zhcosin

  \<#89E3\>\<#7B54\>\<#65E5\>\<#671F\>\<#FF1A\> 2017-02-08

  \<#5148\>\<#63D0\>\<#51FA\>\<#5982\>\<#4E0B\>\<#7684\>\<#5F15\>\<#7406\>\<#FF1A\>

  \<#70B9\><math|P>\<#4E3A\>\<#6B63\>\<#65B9\>\<#5F62\><math|A B C
  D>\<#7684\>\<#8FB9\><math|A B>\<#5916\>\<#4FA7\>\<#4E00\>\<#70B9\>\<#FF0C\><math|P
  C>\<#4E0E\><math|P D>\<#5206\>\<#522B\>\<#4E0E\>\<#8FB9\><math|A
  B>\<#76F8\>\<#4EA4\>\<#4E8E\><math|S>\<#548C\><math|T>\<#FF0C\>\<#8BB0\><math|\<angle\>P
  A B=\<alpha\>>\<#FF0C\><math|\<angle\>P B
  A=\<beta\>>\<#FF0C\>\<#5219\>\<#6709\>\<#FF1A\>

  <\equation*>
    A T:T S:S B =cos\<alpha\>sin\<beta\>:sin\<alpha\>sin\<beta\>
    :sin\<alpha\>cos\<beta\>
  </equation*>

  \<#5229\>\<#7528\>\<#6B64\>\<#5F15\>\<#7406\>\<#5373\>\<#77E5\>\<#FF0C\><math|A
  T:T S>\<#4EC5\>\<#4E0E\>\<#89D2\><math|\<alpha\>>\<#6709\>\<#5173\>\<#FF0C\>\<#56E0\>\<#6B64\>\<#5728\>\<#539F\>\<#9898\>\<#4E2D\>\<#7ACB\>\<#523B\>\<#4FBF\>\<#6709\><math|<frac|A
  S|S P>=<frac|A T|T Q>>\<#FF0C\>\<#6240\>\<#4EE5\>\<#4E24\>\<#7EBF\>\<#5E73\>\<#884C\>\<#3002\>\<#4E0B\>\<#9762\>\<#5C31\>\<#6765\>\<#8BC1\>\<#660E\>\<#8FD9\>\<#4E2A\>\<#5F15\>\<#7406\>\<#FF0C\>\<#8BB0\>\<#70B9\><math|P>\<#5728\>\<#8FB9\><math|A
  B>\<#4E0A\>\<#7684\>\<#6295\>\<#5F71\>\<#4E3A\><math|R>\<#FF0C\>\<#5E76\>\<#5047\>\<#5B9A\>\<#6B63\>\<#65B9\>\<#5F62\>\<#8FB9\>\<#957F\>\<#4E3A\>1\<#FF0C\>

  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  \<#6839\>\<#636E\>\<#6B63\>\<#5F26\>\<#5B9A\>\<#7406\>\<#5373\>\<#6709\>

  <\equation*>
    <frac|a|sin\<alpha\>>=<frac|1|sin<around*|(|\<alpha\>+\<beta\>|)>>=<frac|b|sin\<beta\>>
  </equation*>

  \<#4E8E\>\<#662F\>

  <\equation*>
    a=<frac|sin\<alpha\>|sin<around*|(|\<alpha\>+\<beta\>|)>>,b=<frac|sin\<beta\>|sin<around*|(|\<alpha\>+\<beta\>|)>>
  </equation*>

  \<#6839\>\<#636E\>\<#51E0\>\<#4F55\>\<#5173\>\<#7CFB\>\<#6709\>

  <\equation*>
    A R=b cos\<alpha\>=<frac|sin\<beta\>cos\<alpha\>|sin<around*|(|\<alpha\>+\<beta\>|)>>,P
    R=b sin\<alpha\>=<frac|sin\<alpha\>sin\<beta\>|sin<around*|(|\<alpha\>+\<beta\>|)>>
  </equation*>

  \<#800C\>\<#7531\><math|<frac|T R|A T>=<frac|P R|A D>>\<#5F97\>

  <\equation*>
    A T=<frac|A T|A T+T R>A R=<frac|1|1+<frac|T R|A T>>A
    R=<frac|1|1+<frac|sin\<alpha\>sin\<beta\>|sin<around*|(|\<alpha\>+\<beta\>|)>>>\<cdot\><frac|cos\<alpha\>sin\<beta\>|sin<around*|(|\<alpha\>+\<beta\>|)>>=<frac|cos\<alpha\>sin\<beta\>|sin\<alpha\>sin\<beta\>+sin<around*|(|\<alpha\>+\<beta\>|)>>
  </equation*>

  \<#6839\>\<#636E\>\<#5BF9\>\<#79F0\>\<#6027\>\<#FF0C\>\<#4E92\>\<#6362\><math|\<alpha\>>\<#548C\><math|\<beta\>>\<#53EF\>\<#5F97\>

  <\equation*>
    B S=<frac|sin\<alpha\>cos\<beta\>|sin\<alpha\>sin\<beta\>+sin<around*|(|\<alpha\>+\<beta\>|)>>
  </equation*>

  \<#4E8E\>\<#662F\>

  <\equation*>
    T S=<frac|sin\<alpha\>sin\<beta\>|sin\<alpha\>sin\<beta\>+sin<around*|(|\<alpha\>+\<beta\>|)>>
  </equation*>

  \<#4E8E\>\<#662F\>\<#5F15\>\<#7406\>\<#5F97\>\<#8BC1\>.

  \;
</body>

<\references>
  <\collection>
    <associate|auto-1|<tuple|1|1>>
    <associate|auto-2|<tuple|2|1>>
  </collection>
</references>

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      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-1><vspace|0.5fn>

      <vspace*|1fn><with|font-series|<quote|bold>|math-font-series|<quote|bold>|2<space|2spc>\<#89E3\>\<#7B54\>>
      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
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